Are spacetime horizons higher dimensional sources of energy fields? (The black hole case)

Abstract

We explore the possibility that spacetime horizons in 4D general relativity can be treated as manifestations of higher dimensions that induce fields on our 4D spacetime. In this paper we discuss the black hole event horizon, as an example (we leave the cosmological case for future discussion). Starting off from the field equations of gravity in 5D and some conditions on the metric we construct a spacetime whose imbedding is a 4D generalization of the Schwarzchild metric. The external region of the imbedded spacetime is found to contain two distinct fields. We discuss the properties of the fields and the potential implications. Taken as they are, the results suggest that the collapse of matter to form a horizon may have non-local consequences on the geometry of spacetime. In general, the use of horizon-confined mass as a coordinate suggests three potential features of our universe. The first is that the observed 4D spacetime curvature and ordinary matter fields may be hybrid features of 5D originating from the mixing of coordinates. Secondly, because the fifth coordinate induces physical fields on the 4D hyperface, the global metric of the universe may not be asymptotically flat. And finally, associating matter with an independent dimension points towards a theory of nature that is scale invariant.